Inequality, Costly Redistribution and Welfare in an Open Economy

Inequality, Costly Redistribution and Welfare in an Open Economy Pol Antràs Harvard University Alonso de Gortari Harvard University Oleg Itskhoki Princeton University October 12, 2015 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 1 / 39

Introduction Trade integration raises real income but often increases inequality and might make some worse off Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 2 / 39

Introduction Trade integration raises real income but often increases inequality and might make some worse off Standard approach to demonstrating and quantifying the gains from trade largely ignores trade-induced inequality Kaldor-Hicks compensation principle Two basic shortcomings with this approach: How much compensation/redistribution actually takes place? Is this redistribution costless, as the Kaldor-Hicks approach assumes? Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 2 / 39

Introduction Trade integration raises real income but often increases inequality and might make some worse off Standard approach to demonstrating and quantifying the gains from trade largely ignores trade-induced inequality Kaldor-Hicks compensation principle Two basic shortcomings with this approach: How much compensation/redistribution actually takes place? Is this redistribution costless, as the Kaldor-Hicks approach assumes? These issues are relevant not just for trade, but also for any policy with redistributive effects Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 2 / 39

This Paper We study welfare implications of trade liberalization in a model in which trade affects income distribution...... and in which redistribution policies are constrained by information frictions (Mirrlees, 1971) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 3 / 39

This Paper We study welfare implications of trade liberalization in a model in which trade affects income distribution...... and in which redistribution policies are constrained by information frictions (Mirrlees, 1971) Despite the fact that the tax system is progressive, trade increases inequality in the after-tax distribution of income We propose two types of adjustments to standard welfare measures: 1. A welfarist correction reflecting the preferences of an inequality-averse social planner Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 3 / 39

This Paper We study welfare implications of trade liberalization in a model in which trade affects income distribution...... and in which redistribution policies are constrained by information frictions (Mirrlees, 1971) Despite the fact that the tax system is progressive, trade increases inequality in the after-tax distribution of income We propose two types of adjustments to standard welfare measures: 1. A welfarist correction reflecting the preferences of an inequality-averse social planner 2. A costly-redistribution correction capturing behavioral responses to trade-induced shifts across marginal tax rates Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 3 / 39

A Motivating Graph 14% Openness and Inequality in the United States (1979 2007) 0.60 13% 0.58 12% 0.56 11% 0.54 10% 0.52 9% 0.50 8% 0.48 7% 0.46 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Trade Share Gini of Market Income Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 4 / 39

A Motivating Quote If, as will often happen, the best methods of compensation feasible involve some loss in productive efficiency, this loss will have to be taken into account. Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 5 / 39

A Motivating Quote If, as will often happen, the best methods of compensation feasible involve some loss in productive efficiency, this loss will have to be taken into account. Hicks (1939, p. 712) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 5 / 39

Building Blocks Skeleton of Trade Model: Itskhoki (2008) Melitz (2003) with heterogeneous workers/entrepeneurs and a labor supply decision Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 6 / 39

Building Blocks Skeleton of Trade Model: Itskhoki (2008) Melitz (2003) with heterogeneous workers/entrepeneurs and a labor supply decision Costly Redistribution: Nonlinear progressive tax system After-tax income is log-linear function of pre-tax income (great fit) Welfarist correction: constant degree of inequality- (or risk-) aversion widely used in Public Finance (veil of ignorance rationale) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 6 / 39

Building Blocks Skeleton of Trade Model: Itskhoki (2008) Melitz (2003) with heterogeneous workers/entrepeneurs and a labor supply decision Costly Redistribution: Nonlinear progressive tax system After-tax income is log-linear function of pre-tax income (great fit) Welfarist correction: constant degree of inequality- (or risk-) aversion widely used in Public Finance (veil of ignorance rationale) Model calibrated to fit 2007 U.S. data: distribution of skills calibrated to match U.S. distribution of (adjusted gross) income from IRS public records trade costs calibrated to match U.S. trade share Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 6 / 39

Related Literature Trade models with heterogeneous workers: Itskhoki (2008) but also matching/sorting models (see Grossman, and Costinot and Vogel for surveys) models with imperfect labor markets (Helpman, Itskhoki, Redding..., and earlier Davidson and Matusz) Gains from trade and costly redistribution: Dixit and Norman (1986), Rodrik (1992), Spector (2001), Naito (2006) Old literature on Kaldor-Hicks: Kaldor (1939), Hicks (1939), Scitovszky (1941) Welfarist approach: Bergson (1938), Samuelson (1947), Diamond & Mirlees (1971), Saez more recently Costly-redistribution: Kaplow (2008), Hendren (2014) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 7 / 39

Road Map 1. A Motivating Example 2. 3. Calibration 4. Counterfactuals: Inequality and the Gains from Trade Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 8 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Motivating Example Consider a society composed of a measure one of individuals indexed by an ability ϕ and associated (real) earnings r (ϕ) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 9 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Motivating Example Consider a society composed of a measure one of individuals indexed by an ability ϕ and associated (real) earnings r (ϕ) Agents preferences v defined over (real) disposable income r d (ϕ) = (1 τ (r (ϕ))) r (ϕ) + T (ϕ) where τ (r) is a nonlinear income tax and T (ϕ) a lump-sum transfer The cumulative distribution of ϕ in the population is H (ϕ), while the associated income distribution for real earnings is F (r) Society is evaluating the consequences of a trade liberalization that would shift F (r) from some initial F 0 (r) to F 1 (r). What are the welfare consequences of the move from F 0 (r) to F 1 (r)? Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 9 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction The Kaldor-Hicks Principle: An Illustration Suppose only lump-sum transfers are used and government budget is balanced so T (ϕ) dh (ϕ) = 0 and r d (ϕ) dϕ = rdf (r) The compensating variation for individual of type ϕ associated with trade opening is: v ( r d 1 (ϕ) + CV (ϕ) ) = v ( r d 0 (ϕ) ) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 10 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction The Kaldor-Hicks Principle: An Illustration Suppose only lump-sum transfers are used and government budget is balanced so T (ϕ) dh (ϕ) = 0 and r d (ϕ) dϕ = rdf (r) The compensating variation for individual of type ϕ associated with trade opening is: v ( r d 1 (ϕ) + CV (ϕ) ) = v ( r d 0 (ϕ) ) Hence CV (ϕ) dh (ϕ) = = r1 d (ϕ) dh (ϕ) r0 d (ϕ) dh (ϕ) rdf 1 (r) rdf 0 (r) = R 1 R 0 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 10 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction The Kaldor-Hicks Principle: An Illustration Suppose only lump-sum transfers are used and government budget is balanced so T (ϕ) dh (ϕ) = 0 and r d (ϕ) dϕ = rdf (r) The compensating variation for individual of type ϕ associated with trade opening is: v ( r d 1 (ϕ) + CV (ϕ) ) = v ( r d 0 (ϕ) ) Hence CV (ϕ) dh (ϕ) = = r1 d (ϕ) dh (ϕ) r0 d (ϕ) dh (ϕ) rdf 1 (r) rdf 0 (r) = R 1 R 0 Gains from trade = Aggregate Real Income Growth W 1 = 1 + µ R 1 Kaldor-Hicks W 0 R 0 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 10 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction Pros and Cons of the Kaldor-Hicks Principle Principle does not rely on interpersonal comparisons of utility indirect utility can be heterogeneous across agents result relies on ordinal rather than cardinal preferences notion of efficiency argued to be free of value judgments What if redistribution does not take place and the losers are not compensated? under the veil of ignorance, agents see a probability distribution over potential outcomes (need cardinal preferences) risk aversion inequality aversion Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 11 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction Pros and Cons of the Kaldor-Hicks Principle Principle does not rely on interpersonal comparisons of utility indirect utility can be heterogeneous across agents result relies on ordinal rather than cardinal preferences notion of efficiency argued to be free of value judgments What if redistribution does not take place and the losers are not compensated? under the veil of ignorance, agents see a probability distribution over potential outcomes (need cardinal preferences) risk aversion inequality aversion Even if some redistribution takes place, whenever it is costly, shouldn t W 1 /W 0 reflect those costs? Dixit and Norman (1986) showed that W1/W 0 > 1 using a course set of tax policies - but how large is W 1/W 0? Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 11 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Welfarist Correction Consider an original position in which individuals evaluate policies under a veil of ignorance (not knowing ϕ) Ex-ante symmetry implies that individual/social welfare is V = g ( r d (ϕ) ) dh (ϕ), (1) where g ( ) is concave reflecting risk or inequality aversion Suppose preferences feature constant degree of inequality aversion g ( r d) = ( r d ) 1 ρ 1 1 ρ for ρ 0 (2) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 12 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Welfarist Correction Consider an original position in which individuals evaluate policies under a veil of ignorance (not knowing ϕ) Ex-ante symmetry implies that individual/social welfare is V = g ( r d (ϕ) ) dh (ϕ), (1) where g ( ) is concave reflecting risk or inequality aversion Suppose preferences feature constant degree of inequality aversion g ( ( ) r d) r d 1 ρ 1 = for ρ 0 (2) 1 ρ With simple transformation, we have [ ( (r E ) )] d 1 ρ 1/(1 ρ) W = E (r d E ( r d) = R ) where 1 by Jensen s inequality Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 12 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction Welfarist Correction: Two Special Cases Suppose H (ϕ) is such that the distribution of disposable income is ( Pareto: = { Lognormal: = exp 1+G 1 G(1 2ρ) ) 1/(1 ρ) 1 G 1+G ρ [ Φ 1 ( 1+G 2 )] 2 } where G is the Gini coefficient of the distribution of r d W increases in mean income R but decreases in inequality G Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 13 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction Welfarist Correction: Two Special Cases Suppose H (ϕ) is such that the distribution of disposable income is ( Pareto: = { Lognormal: = exp 1+G 1 G(1 2ρ) ) 1/(1 ρ) 1 G 1+G ρ [ Φ 1 ( 1+G 2 )] 2 } where G is the Gini coefficient of the distribution of r d W increases in mean income R but decreases in inequality G Notice that in both cases W 1 = (G 1; ρ) (1 + µ), (3) Welfarist (G 0 ; ρ) W 0 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 13 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Costly Redistribution Correction Suppose now that lump-sum transfers are not feasible and redistribution has to have through the income tax-transfer system Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 14 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Costly Redistribution Correction Suppose now that lump-sum transfers are not feasible and redistribution has to have through the income tax-transfer system Focus on the particular case (as in Heathcoate et al., 2014) in which 1 τ (r) = k (r) φ, (4) for some constant k which can be set to ensure that the government budget is balanced Average net-of-tax rates decrease in reported income at a constant rate φ, which captures the degree of progressivity of the tax system Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 14 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Costly Redistribution Correction Suppose now that lump-sum transfers are not feasible and redistribution has to have through the income tax-transfer system Focus on the particular case (as in Heathcoate et al., 2014) in which 1 τ (r) = k (r) φ, (4) for some constant k which can be set to ensure that the government budget is balanced Average net-of-tax rates decrease in reported income at a constant rate φ, which captures the degree of progressivity of the tax system Behavioral response to taxation: positive, constant elasticity of reported income to the net-of-marginal-tax rate: ε r 1 τ m (r) > 0 (5) (1 τ m (r)) r Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 14 / 39

Kaldor-Hicks Principle Welfarist Correction Costly Redistribution Correction A Costly Redistribution Correction In such a case, we find that aggregate income can be written as R = (1 φ) ε (Er) 1+ε (Er 1 φ ) ε E (r 1+εφ ) E (r) = Θ R where R is potential revenue (in the absence of distortionary taxes) By Holder s inequality, Θ 1 Θ is reduced by mean preserving multiplicative spreads of the income distribution (increased inequality) Two parametric examples Pareto: Lognormal: Θ = (1 φ) ε (1 φ)(1+g) (1+εφ)2G (1 φ)(1+g) 2G Θ = (1 φ) ε exp { φ2 ε(ε+1) [ ( (1 φ) Φ 1 1+G 2 2 ( ) ε (1 φ)(1 G) (1 φ)(1+g) 2G )] 2 } where G is the Gini of the distribution of disposable income Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 15 / 39

Closed Economy Open Economy Trade and Inequality A Constant Elasticity Model Unit measure of heterogeneous households with ability ϕ H(ϕ) Each household provides its own differentiated good or task (CES) Linear production technology y = ϕl Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 16 / 39

Closed Economy Open Economy Trade and Inequality A Constant Elasticity Model Unit measure of heterogeneous households with ability ϕ H(ϕ) Each household provides its own differentiated good or task (CES) Linear production technology y = ϕl Real market revenue of household ϕ is r aut (ϕ) = Q 1 β y(ϕ) β, (6) where Q is the quantity of final output in the economy Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 16 / 39

Closed Economy Open Economy Trade and Inequality A Constant Elasticity Model Unit measure of heterogeneous households with ability ϕ H(ϕ) Each household provides its own differentiated good or task (CES) Linear production technology y = ϕl Real market revenue of household ϕ is r aut (ϕ) = Q 1 β y(ϕ) β, (6) where Q is the quantity of final output in the economy Households have utility over consumption and labor: u(ϕ) = c(ϕ) 1 γ l(ϕ)γ, γ > 1 (7) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 16 / 39

Closed Economy Open Economy Trade and Inequality A Constant Elasticity Model Unit measure of heterogeneous households with ability ϕ H(ϕ) Each household provides its own differentiated good or task (CES) Linear production technology y = ϕl Real market revenue of household ϕ is r aut (ϕ) = Q 1 β y(ϕ) β, (6) where Q is the quantity of final output in the economy Households have utility over consumption and labor: u(ϕ) = c(ϕ) 1 γ l(ϕ)γ, γ > 1 (7) Consumption equals after-tax income: r(ϕ) T ( r(ϕ) ) = kr(ϕ) 1 φ, (8) and government runs balanced budget Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 16 / 39

Closed Economy Open Economy Trade and Inequality Equilibrium Distribution of disposable income (and utility) is shaped by underlying distribution of ability and by parameters β, γ and φ: where c(ϕ) ϕ β(1+ε)(1 φ) 1+εφ ε β γ β governs the elasticity of market income to marginal tax rates Higher after-tax income inequality when income is more elastic to taxes (higher ε) taxes are less progressive (higher φ) tasks are more substitutable (higher β) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 17 / 39

Closed Economy Open Economy Trade and Inequality Social Welfare With a constant degree of inequality aversion ρ, we can write W = ˆΘ W where [ ( (r E ) )] d 1 ρ 1/(1 ρ) = E (r d ) [ ˆΘ = (1 + εφ) (1 φ) εκ (Er) 1+ε (Er 1 φ ) ε E (r 1+εφ ) ] κ and κ = 1/ (1 (1 β)(1 + ε)) > 1. is the same welfarist correction as in our example ˆΘ is a slightly modified costly-redistribution correction W is welfare in a hypothetical Kaldor-Hicks economy Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 18 / 39

Closed Economy Open Economy Trade and Inequality A First Look at the Data 1.5 1.4 Real Adjusted Gross Income in the United States (1979-2007) Mean Income Median Income 10 th Percentile 1.3 1.2 1.1 1 0.9 0.8 1980 1985 1990 1995 2000 2005 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 19 / 39

Closed Economy Open Economy Trade and Inequality Calibration: U.S. Income Growth (1979-2007) Use U.S. Individual Income Tax Public Use Sample to calibrate distribution of market income approximately 3.5 million anonymized tax returns use NBER weights to ensure this is a representative sample we map market income to adjusted gross income in line 37 of IRS Form 1040 Use CBO data on before-tax and after-tax/transfer income to calibrate the degree of tax progressivity φ Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 20 / 39

Closed Economy Open Economy Trade and Inequality Calibration: U.S. Income Growth (1979-2007) Use U.S. Individual Income Tax Public Use Sample to calibrate distribution of market income approximately 3.5 million anonymized tax returns use NBER weights to ensure this is a representative sample we map market income to adjusted gross income in line 37 of IRS Form 1040 Use CBO data on before-tax and after-tax/transfer income to calibrate the degree of tax progressivity φ Elasticity of substitution = 4 (β = 3/4) BEJK (2003), Broda and Weinstein (2006) Experiment with various values of ε and ρ Benchmark ε = 0.5 and ρ = 1 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 20 / 39

Closed Economy Open Economy Trade and Inequality Calibrating the Income Distribution Lognormal provides a reasonably good approximation, but it does a poor fit for the right-tail of the distribution, which looks Pareto 1 Income Distribution CDF 2.5 Empirical Pareto Coefficient 0.9 Data (Non-Parametric Fit) Lognormal Fit 0.8 0.7 2 0.6 0.5 0.4 0.3 1.5 0.2 0.1 0 6 8 10 12 r 1 0 1 2 3 4 5 r #10 5 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 21 / 39

Closed Economy Open Economy Trade and Inequality Calibrating Tax Progressivity Equation (4) may seem ad hoc, but it fits U.S. data remarkably well (similar fit with PSID data) 14 Log Income After Taxes and Transfers 13 12 11 10 y = 0.818x + 2.002 R² = 0.988 9 9 10 11 12 13 14 Log Market Income Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 22 / 39

Closed Economy Open Economy Trade and Inequality U.S. Progressivity Over Time Degree of Progressivity 0.1.2.3.4 1979 1983 1987 1991 1995 1999 2003 2007 Year Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 23 / 39

Closed Economy Open Economy Trade and Inequality Evolution of and ˆΘ Over Time 0.93 (",(1+0? )# 5 ) Phase Diagram, ;=1, 0 =0.5 0.92 0.91 (1+0?)# 5 : Costly Redistribution 0.9 0.89 0.88 0.87 0.86 0.85 0.55 0.6 0.65 0.7 0.75 0.8 ": Inequality Aversion Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 24 / 39

Closed Economy Open Economy Trade and Inequality Social Welfare and Counterfactuals Mean real income grew 44.2% over 1979-2007, or 1.32% per year. For the logarithmic case (ρ = 1), the implied annual growth rate in social welfare is down to 0.34%. Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 25 / 39

Closed Economy Open Economy Trade and Inequality Social Welfare and Counterfactuals Mean real income grew 44.2% over 1979-2007, or 1.32% per year. For the logarithmic case (ρ = 1), the implied annual growth rate in social welfare is down to 0.34%. partly due to observed decline in progressivity By how much would real income and social welfare have increased if φ had been held constant at its 1979 level? For ρ = 1 and ε = 0.5 : real disposable income would have instead grown by 0.89% per year social welfare by 0.49% per year Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 25 / 39

Closed Economy Open Economy Trade and Inequality Social Welfare and Counterfactuals Mean real income grew 44.2% over 1979-2007, or 1.32% per year. For the logarithmic case (ρ = 1), the implied annual growth rate in social welfare is down to 0.34%. partly due to observed decline in progressivity By how much would real income and social welfare have increased if φ had been held constant at its 1979 level? For ρ = 1 and ε = 0.5 : real disposable income would have instead grown by 0.89% per year social welfare by 0.49% per year By how much would real income and social welfare have increased if φ had kept at its 1979 level? For ρ = 1 and ε = 0.5 : real disposable income would have instead grown by 0.35% per year social welfare by 0.48% per year Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 25 / 39

Closed Economy Open Economy Trade and Inequality Open Economy: Environment Consider a world economy with N + 1 symmetric countries Agents can market their output locally or in any of the other N countries Trade/Offshoring involves two types of additional costs 1. Symmetric iceberg cost τ (reduces revenue per unit shipped) 2. Fixed cost of exporting f (n) increasing in the number n of foreign markets served f (n) = f x n α (in terms of final output) helps smooth effect of trade integration on the income distribution Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 26 / 39

Closed Economy Open Economy Trade and Inequality Open Economy: Environment Consider a world economy with N + 1 symmetric countries Agents can market their output locally or in any of the other N countries Trade/Offshoring involves two types of additional costs 1. Symmetric iceberg cost τ (reduces revenue per unit shipped) 2. Fixed cost of exporting f (n) increasing in the number n of foreign markets served f (n) = f x n α (in terms of final output) helps smooth effect of trade integration on the income distribution Sale revenue is now where and y(ϕ) = ϕl (ϕ) is total output r(ϕ) = Υ 1 β n(ϕ) Q1 β y(ϕ) β, (9) Υ n(ϕ) = 1 + n (ϕ) τ β 1 β Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 26 / 39

Closed Economy Open Economy Trade and Inequality Open Economy: Taxation Assume again that the government only observes market revenue of individuals and taxes according to the tax schedule T (r) in (4) government does not observe exporting decisions and f (n (ϕ)) is not tax deductible Disposable income or consumption is thus c(ϕ) = r(ϕ) T ( r(ϕ) ) f x n (ϕ) α. (10) Agents now choose labor input l(ϕ) and market access investment n(ϕ) to maximize utility (7) given the revenue function (6) and budget constraint (10) Given symmetry, goods market clearing imposes ( 1 Q = 0 Υ 1 β n(ϕ) y(ϕ)β )1/β (11) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 27 / 39

Closed Economy Open Economy Trade and Inequality Trade and Inequality Result: Trade increases inequality of revenues and utilities c (ϕ) Q ϕ β(1+ε)(1 φ) 1+εφ, ϕ < ϕ x1, (1 β)(1+ε)(1 φ) 1+εφ Υ1 ϕ β(1+ε)(1 φ) 1+εφ, ϕ < ϕ x2,.. Υ n = 1+nτ β 1 β (1 β)(1+ε)(1 φ) 1+εφ ΥN ϕ β(1+ε)(1 φ) 1+εφ ϕ ϕ xn Two limiting cases: no agent exports (ϕx1 ) all agents export (ϕxn ϕ min ) c (ϕ) Q caut (ϕ) = ϕ β(1+ε)(1 φ) 1+εφ Q aut Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 28 / 39

Relative Revenues, r/r A Motivating Example Closed Economy Open Economy Trade and Inequality Trade and Inequality (cont.) Trade increases relative sale revenue of high-ability households but reduces that of low-ability households 6 5 Autarky Open Economy 4 3 2 1 0 0 100 200 300 400 500 600 700 800 900 1000 Productivity Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 29 / 39

Closed Economy Open Economy Trade and Inequality Trade and Inequality (cont.) 1.035 1.03 1.025 1.02 1.015 1.01 1.005 Gini Ratio, N=1 Pre-Tax Post-Tax Variance(R/mean(R)) Ratio, N=1 1.07 1.06 1.05 1.04 1.03 1.02 1 1 1.5 2 2.5 Variable Trade Cost = 1.01 1 1.5 2 2.5 Variable Trade Cost = 1.12 1.1 1.08 1.06 1.04 1.02 Gini Ratio, N=10 Variance(R/mean(R)) Ratio, N=10 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1 1 1.5 2 2.5 Variable Trade Cost = 1.2 1 1.5 2 2.5 Variable Trade Cost = Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 30 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction : Road Map We first calibrate the model to 2007 U.S. data (trade share, income distribution, tax progressivity) We then explore the implication of a move to autarky on 1. Aggregate Income 2. Income Inequality We use the model to gauge the quantitative importance of the two corrections developed above 1. How large are the gains from trade for different degrees of inequality aversion? Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 31 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction : Road Map We first calibrate the model to 2007 U.S. data (trade share, income distribution, tax progressivity) We then explore the implication of a move to autarky on 1. Aggregate Income 2. Income Inequality We use the model to gauge the quantitative importance of the two corrections developed above 1. How large are the gains from trade for different degrees of inequality aversion? 2. How large would the gains from trade be in the absence of costly redistribution (i.e., φ = 0)? Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 31 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Calibration Hold the following parameters fixed 1. Elasticity of substitution = 4 (β = 3/4) as before 2. Iceberg trade costs (τ = 1.83) Melitz and Redding (2014), Anderson and Van Wincoop (2004) 3. Number of countries (N = 10) U.S. roughly 10-15% of world GDP; results not too sensitive to N above 5 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 32 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Calibration Hold the following parameters fixed 1. Elasticity of substitution = 4 (β = 3/4) as before 2. Iceberg trade costs (τ = 1.83) Melitz and Redding (2014), Anderson and Van Wincoop (2004) 3. Number of countries (N = 10) U.S. roughly 10-15% of world GDP; results not too sensitive to N above 5 Set baseline fixed cost f x to match a U.S. trade share of 0.14 Set convexity of fixed costs to either α = 1 or α = 3 (consistent with preliminary estimates exploiting cross-section of U.S. exports) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 32 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Calibration: Progressivity Note from (4) that ln r d = ln k + (1 φ) ln r (ϕ) = φ = 0.147 Log Income After Taxes and Transfers, 2007 14.5 13.5 12.5 11.5 10.5 y = 0.853x + 1.661 R² = 0.995 9.5 9.5 10.5 11.5 12.5 13.5 14.5 Log Market Income, 2007 Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 33 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Calibrated Welfare Gains from Trade and Inequality Calibrated welfare gains from trade are higher, the higher is the labor supply elasticity ε (Arkolakis and Esposito, 2014) But relative to autarky trade induces more inequality when ε is high Gains from Trade Increase in Gini Coefficient Labor supply elasticity α = 1 α = 3 α = 1 α = 3 ε = 0 4.86% 4.02% 2.31% 1.70% ε = 0.1 5.52% 4.54% 2.44% 1.81% ε = 0.25 6.54% 5.36% 2.64% 1.95% ε = 0.5 8.31% 6.77% 2.92% 2.17% ε = 0.75 10.40% 8.32% 3.16% 2.35% ε = 1 12.41% 9.89% 3.36% 2.51% ε = 1.5 16.72% 13.21% 3.72% 2.78% Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 34 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Welfarist Correction Welfarist correction is higher, the higher is risk/inequality aversion ρ and the lower is the labor supply elasticity ε With log utility (ρ = 1) and a labor supply elasticity of ε = 0.5, welfare gains are 21% lower for both α = 1 and α = 3 1.00 Welfarist Adjustment ( ) 1.00 Welfarist Adjustment ( =3) 0.95 0.95 0.90 0.90 0.85 0.85 0.80 0.80 0.75 0.75 0.70 0.70 0.65 0.65 0.60 0 0.1 0.25 0.5 0.75 1 2 Degree of Risk/Inequality Aversion ( ) 0.60 0 0.1 0.25 0.5 0.75 1 2 Degree of Risk/Inequality Aversion ( ) Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 35 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Costly Redistribution Correction Costly redistribution correction is higher, the higher is the labor supply elasticity ε When ε = 0.5, welfare gains are 21% lower for α = 1 and 16% lower for α = 3 1.00 0.95 0.90 0.85 Costly Redistribution Correction ( =0) 0.80 0.75 0.70 0.65 0.60 Elasticity of Labor Supply Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 36 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Nonparametric versus Lognormal Case Lognormal underpredicts costly redistribution correction, especially for high ε (underpredicts the behavior of the right tail) 1 Nonparametric vs. Lognormal Costly Redistribution Correction ( =0) Nonparametric Distribution 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Lognormal Distribution Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 37 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Optimal Progressivity and Implied Inequality Aversion The observed degree of progressivity in 2007 is optimal if ρ is around 0.7 0.25 0.2 Progressivity of taxation, φ 0.15 0.1 0.05 Autarky Trade Equilibrium 0 0 0.2 0.4 0.6 0.8 1 Inequality aversion, ρ Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 38 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Conclusions Trade-induced inequality is partly mitigated via a progressive income tax system Still, compensation is not full so trade induces an increase in the distribution of disposable income Is it so clear that the Kaldor-Hicks principle is free of value judgements in that case? Income taxation induces behavioral responses that affect the aggregate income response to trade integration Shouldn t the Kaldor-Hicks principle adjust for this leaky bucket effect? Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 39 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Conclusions Trade-induced inequality is partly mitigated via a progressive income tax system Still, compensation is not full so trade induces an increase in the distribution of disposable income Is it so clear that the Kaldor-Hicks principle is free of value judgements in that case? Income taxation induces behavioral responses that affect the aggregate income response to trade integration Shouldn t the Kaldor-Hicks principle adjust for this leaky bucket effect? In this paper, we have developed welfarist and costly redistribution corrections to standard measures of the gains from trade integration Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 39 / 39

Calibration Calibrated Welfarist Correction Calibrated Costly Redistribution Correction Conclusions Trade-induced inequality is partly mitigated via a progressive income tax system Still, compensation is not full so trade induces an increase in the distribution of disposable income Is it so clear that the Kaldor-Hicks principle is free of value judgements in that case? Income taxation induces behavioral responses that affect the aggregate income response to trade integration Shouldn t the Kaldor-Hicks principle adjust for this leaky bucket effect? In this paper, we have developed welfarist and costly redistribution corrections to standard measures of the gains from trade integration Under plausible parameter values, these corrections are nonneglible and eliminate about one-fifth of the (static) gains from trade Antràs, de Gortari and Itskhoki Inequality, Costly Redistribution and Welfare in an Open Economy 39 / 39